Abstract: The autoregressive neural networks are emerging as a powerful computational tool to solve relevant problems in classical and quantum mechanics. One of their appealing functionalities is that, after they have learned a probability distribution from a dataset, they allow exact and efficient sampling of typical system configurations. Here we employ a neural autoregressive distribution estimator (NADE) to boost Markov chain Monte Carlo (MCMC) simulations of a paradigmatic classical model of spin-glass theory, namely, the two-dimensional Edwards-Anderson Hamiltonian. We show that a NADE can be trained to accurately mimic the Boltzmann distribution using unsupervised learning from system configurations generated using standard MCMC algorithms. The trained NADE is then employed as smart proposal distribution for the Metropolis-Hastings algorithm. This allows us to perform efficient MCMC simulations, which provide unbiased results even if the expectation value corresponding to the probability distribution learned by the NADE is not exact. Notably, we implement a sequential tempering procedure, whereby a NADE trained at a higher temperature is iteratively employed as proposal distribution in a MCMC simulation run at a slightly lower temperature. This allows one to efficiently simulate the spin-glass model even in the low-temperature regime, avoiding the divergent correlation times that plague MCMC simulations driven by local-update algorithms. Furthermore, we show that the NADE-driven simulations quickly sample ground-state configurations, paving the way to their future utilization to tackle binary optimization problems.

Abstract: We report morpho-structural properties and charge conduction mechanisms of a foamy “graphene sponge ”, having a density as low as & AP;0.07 kg/m3 and a carbon to oxygen ratio C:O & SIME; 13:1. The spongy texture analysed by scanning electron microscopy is made of irregularly-shaped millimetres-sized small flakes, containing small crystallites with a typical size of & SIME;16.3 nm. A defect density as high as & SIME;2.6 x 1011 cm-2 has been estimated by the Raman intensity of D and G peaks, dominating the spectrum from room temperature down to & SIME;153 K. Despite the high C:O ratio, the graphene sponge exhibits an insulating electrical behavior, with a raise of the resistance value at & SIME;6 K up to 5 orders of magnitude with respect to the room temperature value. A variable range hopping (VRH) conduction, with a strong 2D character, dominates the charge carriers transport, from 300 K down to 20 K. At T < 20 K, graphene sponge resistance tends to saturate, suggesting a temperature-independent quantum tunnelling. The 2D-VRH conduction originates from structural disorder and is consistent with hopping of charge carriers between sp2 defects in the plane, where sp3 clusters related to oxygen functional groups act as potential barriers.</p>